Interaction of two shallow non-circular tunnels with imperfect interfaces subjected to shear waves

The dynamic interaction of two non-circular shallow tunnels with imperfect interfaces subjected to anti-plane waves is investigated, and the semi-analytical solution of dynamic stress with the half-plane boundary effect is presented. The spring model is adopted to analyse the effect of imperfect interfaces between the tunnel and the rock mass on the dynamic stress. The half-plane boundary is modelled by an arc with a large radius to satisfy the traction-free boundary condition. Combining the wave function expansion method and conformal transformation method, the analytical solutions of stresses and displacements are expanded in terms of wave functions. The expanded coefficients are determined by satisfying the imperfect boundary conditions around the tunnels and the traction-free boundary condition at the surface. Some numerical examples are provided to discuss the imperfect interface effects on the dynamic stress under different depths of tunnels and different distances between the two tunnels. Comparison with existing numerical results validates this present dynamic model.